Quantile regression in high-dimension with breaking

DOI

10.2991/jsta.2013.12.3.6How to use a DOI?

Keywords

change-points; high-dimension; oracle properties; SCAD; LASSO-type estimators

Abstract

The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed errors is considered. In this case, least square method with LASSO or adaptive LASSO penalty can not be used since the theoretical assumptions do not occur or the estimators are not robust. Then, the quantile model with SCAD penalty or median regression with LASSO-type penalty allows, in the same time, to estimate the parameters on every segment and eliminate the irrelevant variables. We show that, for the two penalized estimation methods, the oracle properties is not affected by the change-point estimation. Convergence rates of the estimators for the change-points and for the regression parameters, by the two methods are found. Monte-Carlo simulations illustrate the performance of the methods.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Gabriela Ciuperca
PY  - 2013
DA  - 2013/09/01
TI  - Quantile regression in high-dimension with breaking
JO  - Journal of Statistical Theory and Applications
SP  - 288
EP  - 305
VL  - 12
IS  - 3
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2013.12.3.6
DO  - 10.2991/jsta.2013.12.3.6
ID  - Ciuperca2013
ER  -